How do you find the #lim_(xrarr3) (x^2+x-12)/(x-3)#?

3 Answers
Apr 16, 2017

#7#

Explanation:

Rewrite the numerator as #(x+4)(x-3)#

#lim_(x->3) ((x+4)(x-3))/(x-3)#

Cancel the #x-3#

#lim_(x->3) x+4#

Plug in #3# for #x#:

#3+4=7#

Apr 16, 2017

The numerator factors and cancels the denominator, leaving a simple linear expression that can be evaluated at the limit.

Explanation:

Given: #lim_(xrarr3) (x^2+x-12)/(x-3)#

Factor the numerator:

#lim_(xrarr3) ((x-3)(x+4))/(x-3)#

Please observe the factors that cancel:

#lim_(xrarr3) (cancel(x-3)(x+4))/cancel(x-3)#

This leaves a simple linear expression that can be evaluated at the limit:

#lim_(xrarr3) x+4 = 7#

Apr 16, 2017

#7#

Explanation:

#"factorise numerator and simplify"#

#lim_(xto3)((x+4)(cancel(x-3)))/(cancel(x-3))#

#=lim_(xto3)(x+4)=3+4=7#